The present invention relates to a mark detection method, an exposure method, a device manufacturing method, a mark detection apparatus, and an exposure apparatus. More particularly, the present invention relates to a mark detection method for detecting a mark for position measurement that is formed on an object such as a semiconductor substrate or a liquid crystal display device, an exposure method for transferring a predetermined pattern on a substrate aligned by the use of the mark detection method, a device manufacturing method using the exposure method, a mark detection apparatus for detecting a mark for position measurement which is formed on an object such as a semiconductor substrate or a liquid crystal display device, an exposure apparatus for transferring a predetermined pattern onto a substrate aligned by the mark detection apparatus, and a device manufactured by the exposure apparatus.
In manufacturing a semiconductor device and a liquid crystal display device, a variety of planar techniques are utilized. In the planar techniques, a finely patterned image formed on a photomask and a reticle (hereinafter, referred to as reticle) by the use of an exposure apparatus is projected and exposed on a substrate such as a semiconductor wafer or glass plate on which a photosensitive agent such as photoresist is coated (hereinafter, referred to as wafer).
The reticle pattern is projected and exposed by the use of, for example, an exposure apparatus of a step-and-repeat system in such a manner that a position of the reticle and a position of the wafer are adjusted (aligned) with high accuracy and the reticle pattern is superposed on a pattern already formed on the wafer.
Particularly in recent years, high densification has been required for semiconductor circuits. Accordingly, also in the alignment of the exposure apparatus, as the pattern of the semiconductor circuit or the like becomes finer, a demand for an alignment performed with higher accuracy has increased, and various processes for alignment have been made.
In general, the alignment of the reticle is performed using exposure light.
Among alignment systems for the reticle, there is a Visual Reticle Alignment (VRA) system or the like, in which an alignment mark drawn on a reticle is irradiated with exposure light, and image data of the alignment mark picked up by a CCD camera or the like is subjected to image processing, and a mark position is measured.
The following are types of alignment sensors for wafers.
(1) Laser Step Alignment (LSA)
This sensor is a sensor for irradiating alignment marks arranged as a line of dots on a wafer with a laser beam in order to detect a mark position by the use of light diffracted or scattered by the mark.
(2) Field Image Alignment (FIA)
This sensor is a sensor for irradiating alignment marks arranged as a line of dots with light having a large wavelength bandwidth using a halogen lamp or the like as a light source, and performing image processing of the image data of an alignment mark imaged by a CCD camera or the like in order to measure a mark position.
(3) Laser Interferometric Alignment (LIA)
This sensor is a sensor for irradiating alignment marks arranged in a diffraction grating pattern on a wafer from two directions using laser beams having slightly different frequencies and causing the two generated diffraction lights to interfere with each other in order to measure a position of the alignment mark from the phase obtained through the interference.
In the alignment by these optical systems, first, an alignment mark on the reticle is detected and processed to measure a position coordinate thereof. Next, an alignment mark on the wafer is detected and processed to measure a position coordinate thereof, thus position of a shot to be superposed is determined. Based on these results, the wafer is moved by a wafer stage to perform an alignment so that a pattern image of the reticle can be superposed on the shot position, and the pattern image of the reticle is projected and exposed on the wafer.
In some of the above-described alignment systems, processing is performed after a one-dimensional image or a two-dimensional image is obtained as an alignment signal.
For the case of a two-dimensional image, by adding mark portions in the measured direction, it can also be treated as a one-dimensional image.
These signals are originally signals that are continuously distributed with respect to the position, but for convenience of signal transmission of an image pickup device, the signals will be extracted as signals sampled at a predetermined interval. For example, when an image processing sensor, such as a CCD camera or a line sensor, is used as an image pickup device, since the pixel size is limited, the signals will be sampled at an interval determined by the pixel size. Ideally, it is desirable that signals output from the image pickup device be sampled by a sampling apparatus at an interval corresponding to the pixel size of the image pickup device.
Edge detection, a correlation method or the like is used for these sampled signals in order to measure the mark position.
Incidentally, in general, the accuracy required for the alignment sensor is extremely high in comparison to the minimum resolving unit of the image pickup device. For this reason, the position must be finally determined with an accuracy equal to or less than the sampled interval.
Heretofore, in edge detection and the correlation method, processing has been performed for the sampled signals, and when the final position result is calculated, the interval between the sampled points is fitted by an appropriate function such as a linear or a quadratic function, and by solving the function, a resolving power less than the sampled interval has been obtained. Typically, the finer the sampling interval, the more the accuracy is improved.
On the other hand, when the magnification of the optical system is increased in order to reduce the sampled interval on an object, the visual field is narrowed due to a limitation in the number of pixels of the CCD camera.
Considering the constitution of the apparatus, the visual field of the sensor must be ensured to some extent by conditions such as size of the alignment mark or the accuracy of the pre-alignment performed before the alignment measurement.
In addition, in order to prevent the conversion of a high-frequency component of a signal into a low-frequency component by sampling (aliasing), a necessary condition is that the minimum resolving unit of the image in the image pickup device is 0.5 times or less of the minimum periodic component.
The minimum periodic component of the signal is given by, for example, in the case of an image processing sensor using an optical microscope, the lower limit of the minimum periodic component of the image as Pmin as follows:
Pmin=xcex(2xc3x97NA)
xcex: wavelength of light
NA: NA of optical system
However, this value will also vary depending on the illumination conditions. By using this value, the sampling interval Ps is given as:
Ps less than 0.5xc3x97Pmin
and, the above-described conditions can be satisfied.
However, when the sampling interval P, is increased, the error in sampling when performing the edge measurement or correlation measurement becomes significantly worse before the sampling interval Ps reaches 0.5xc3x97Pmin, that is, from about 0.2xc3x97Pmin.
FIG. 14 is a diagram for explaining the process during the execution of the edge detection.
In a typical edge detection algorithm, first, the point of maximum inclination, slope point is found. Typically, since the sampling interval is a fixed value, a point is obtained where a difference xcex94V between adjacent sampled points in the V direction in the drawing is at a maximum. In the example of FIG. 14, the point denoted by the reference symbol P0 is the point of maximum inclination.
From this point, the closest relative maximum and minimum are found by hill-climbing and hill-descending. In the example shown in FIG. 14, with reference symbol P0 as a center, points are found in the H1 and H2 directions where the difference xcex94V in the V direction in the drawing becomes a minimum. These points are defined to be the maximum value and the minimum value of the edge. In the example of FIG. 14, the sampled point P1 becomes the maximum value of the edge, and the sampled point P2 becomes the minimum value of the edge.
After the maximum value and the minimum value of the edge are obtained, setting a slice level SL as, for example, an intermediate value of these values, the edge positions E1 and E2 are set as the points where the edge crosses the slice level.
When the sampling interval is increased to some extent, the maximum value and the minimum value of the above-described edge will vary according to the relationship between the sampled position and the signal edge position. For this reason, the slice level SL varies, resulting in a variation of the measurement result.
In addition, since the fitting is performed by a linear function, a quadratic function, or the like, when obtaining the edge positions E1 and E2, an error occurs here also.
Also in the correlation method, depending on the positional relationship between the sampled position and the signal, the mark signal causes deformation so as to change the center of gravity thereof, resulting in a variation in the measurement result.
Moreover, also in the correlation method, since a resolving power which is smaller than the sampled interval results from the fitting to a quadratic or the like, an interpolation error occurs here also.
Furthermore, heretofore, in order to improve the accuracy, a plurality of marks have been typically used for the alignment marks, and the accuracy has also been improved by averaging of the respective marks obtained by sampling in different phases.
Incidentally, when performing superposition by an exposure apparatus, a shift of the image according to the structure of the alignment mark and resulting from a comatic aberration becomes a problem. However, it has recently been found that the comatic aberration can be improved by increasing NA.
In addition, since the measurement accuracy improves as the edge slope becomes steeper for a signal which has a noise at the same level, it is also necessary to increase NA of the optical system used in the alignment in order to improve the alignment accuracy.
However, when NA of the alignment optical system is increased, a problem occurs in that the minimum periodic component Pmin included in the image, that is,
Pmin=xcex(2xc3x97NA)
decreases as NA increases.
Since it is difficult to narrow the visual field under the present situation, it has become difficult to satisfy the condition of Ps less than 0.2xc3x97Pmin.
In addition, in using an XY-simultaneous mark for measuring X and Y simultaneously in order to increase speed (refer to the gazette of Japanese Unexamined Patent Application, First Publication No. Hei 2-272305 for details), the number of alignment marks must be reduced, and thus the above-described averaging effect also decreases.
Hereinbelow, simulation results will be used to describe the relationship between the sampling interval and the position measurement error.
FIGS. 15 and 16 are diagrams showing position measurement errors when sampling is performed for a step difference mark of a 6 xcexcm line for different sampling intervals. FIG. 15 is a diagram showing position measurement errors when imaging is performed with an optical system having a wavelength of 0.6 xcexcm, an illumination sigma=1, and NA=0.6. FIG. 16 is a diagram showing position measurement errors when imaging is performed with an optical system having a wavelength of 0.6 xcexcm, an illumination sigma=1 and NA=0.3. In FIGS. 15 and 16, the abscissa shows sampling intervals, and the ordinate shows position measurement errors.
In this simulation, the minimum periodic component Pmin included in the above-described image is 1 xcexcm when NA is 0.3 and 0.5 xcexcm when NA is 0.6.
As shown in FIGS. 15 and 16, when the sampling interval is changed, a result is obtained wherein the position measurement errors are cyclically reduced. However, this sampling interval in which the position measurement errors are reduced changes depending on the line width.
In alignment of the exposure apparatus and the like, the total required overlay (total overlay accuracy) also varies depending on the line width of the circuit pattern printed on the substrate. However, for this total overlay, typically an accuracy of xc2xc or less of the minimum line width of the printed circuit pattern is required. An accuracy of about 50 nm is typically required for the total overlay. In order to satisfy this requirement, the measurement error allowable for the alignment sensor is about 3 to 5 nm.
Now, the alignment error allowable for alignment is assumed to be 5 nm.
As is apparent from FIGS. 15 and 16, even if NA is 0.6 and 0.3, when the sampling interval Ps is 0.2xc3x97Pmin less than Ps less than 0.39xc3x97Pmin, and when the sampling interval Ps is Ps greater than 0.41xc3x97Pmin, the point measurement error exceeds the allowable error.
FIG. 17 is a diagram showing the simulation results representing the relationship between the sampling interval and the position measurement error when a normalized mutual correlation is used.
As shown in FIG. 17, as the sampling interval Ps becomes longer, the position measurement errors smoothly increase, and, with about Ps less than 0.2xc3x97Pmin as a reference, the deterioration of the accuracy cannot be permitted.
Next, the results obtained by performing the edge detection with an increase in the number of alignment marks will be shown.
FIGS. 18 to 20 are diagrams showing the simulation results representing the relationship between the sampling interval and the position measurement error when the number of alignment marks is changed. FIG. 18 is a diagram showing the result when the number of line spaces (hereinafter referred to as LandS) is three; FIG. 19 is a diagram showing the result when LandS is six; and FIG. 20 is a diagram showing the result when LandS is nine.
In general, as the number of alignment marks is increased, the position measurement error decreases. However, from the results shown in FIGS. 18 to 20, it is understood that there is a sampling interval where the position measurement error does not decrease very much even if the number of alignment marks is increased.
Moreover, with reference to FIGS. 18 to 20, sampling intervals cyclically appear at which the position measurement errors are extremely reduced. The magnification of the optical system may be set so that the sampling interval thereof can be matched to the above-described sampling interval. However, this is not so desirable because the magnification accuracy during manufacturing needs to be made strict and different mark intervals cannot be dealt with.
The present invention was made in consideration of the foregoing circumstances in mind. The object of the present invention is to provide, even if a sampling interval must be set to about 0.2 times or more of the lower limit of the minimum periodic component, a mark detection method capable of reducing a position error of a mark position, an exposure method for transferring a predetermined pattern onto a substrate aligned using the mark detection method, a device manufacturing method using the exposure method, a mark detection apparatus, an exposure apparatus for transferring a predetermined pattern onto a substrate aligned using the mark detection apparatus, and a device manufactured by the use of the exposure apparatus.
Another object of the present invention is to provide, even if the sampling interval is equal to 0.5 times or more of the lower limit of the minimum periodic component, that is, even if the sampling interval does not satisfy a sampling theorem, a mark detection method capable of preventing a position measurement error caused by aliasing, an exposure method for transferring a predetermined pattern onto a substrate aligned using the mark detection method, a device manufacturing method using the exposure method, a mark detection apparatus, an exposure apparatus for transferring a predetermined pattern onto a substrate aligned using the mark detection apparatus and a device manufactured using the exposure apparatus.
In order to accomplish the foregoing objects, a first mark detection method of the present invention comprises the steps of: irradiating a mark formed on an object with a detection beam; imaging an image of the mark through an image-forming system; converting the image of the mark which is formed on an image pickup device into an electrical image signal; outputting a signal related to the image signal in a predetermined sampling interval; and interpolating the signals related to the image signal in cycles equal to or less than the predetermined sampling intervals.
According to this invention, in the case where the minimum resolution unit of an image pickup device must be 0.2 times the minimum periodic component of an image or more, there is an advantage that the position measurement error of a mark can be significantly reduced by interpolating in a cycle equal to or less than a predetermined sampling interval for image signals of the mark which are sampled at the predetermined intervals.
In addition, in the above-described mark detection method, the image pickup device has a predetermined pixel size, the predetermined sampling interval includes an interval of the predetermined pixel size, and the interpolation is performed at an interval equal to or less than the predetermined pixel size. In this case, the pixel size is preferably a predetermined multiple of the minimum periodic component of the image formed on the image pickup device. This minimum periodic component is defined by xcex/2NA based on the wavelength xcex of the detection beam and the numerical aperture NA of the imaging system. Moreover, it is preferable that the pixel size be 0.2 times the minimum periodic component or more and, further, 0.5 times the minimum periodic component or less. In this case, it is best if the pixel size is anywhere between 0.39 times or more to 0.41 times or less of the minimum periodic component. Moreover, it is preferable to perform a smoothing operation to remove a component equal to or less than a predetermined cycle from the image signal output at the sampling intervals.
Furthermore, it is preferable that the smoothing operation remove a periodic component equal to or less than 1/(1/Psxe2x88x921/Pmin), which is represented by the predetermined pixel size Ps and the minimum periodic component Pmin.
By performing this processing, aliasing noise can be removed in the case where the minimum resolving unit Ps of the image pickup device must be 0.5 times or more of the minimum periodic component Pmin of the image; thus there is an advantage that error accuracy can be improved even in conditions where the image of an object cannot be completely restored.
As a result, since the position measurement in a coarse sampling interval can be performed on, for example, the image of the alignment mark, the expansion of NA or the expansion of the visual field is possible even by the use of a conventional image pickup device.
Moreover, since an interpolation operation accompanied with smoothing is performed in this invention, there is an advantage in that processing time can be shortened as compared with the case where interpolation and low pass filtering are performed separately.
Furthermore, the predetermined pixel size Ps is preferably more than 0.5 times the minimum periodic component Pmin.
Specifically, the smoothing operation comprises: a step of setting a smoothing point where smoothing is performed for the image signal; a step of selecting, from the image signal, an image signal sampled in a predetermined range that includes the smoothing point; a step of sampling a function while removing a periodic component smaller than 1/(1/Psxe2x88x921/Pmin) according to the distance between the position of the smoothing point and a position of the selected image signal in a cycle identical to the sampling interval of the image signal; and a step of adding the product of the selected image signal and the sampled function, the product being obtained for each of the image signals included in the predetermined range. Alternatively, the smoothing operation comprises: a step of setting an interpolation point where the interpolation for the image signal is to be performed; a step of obtaining a most proximate position of the image signal, which is most proximate to the position of the interpolation point; a step of selecting, from the image signal, an image signal sampled in a predetermined range including the most proximate position; and a step of adding the product of the selected image signal and the function removing a periodic component smaller than 1/(1/Psxe2x88x921/Pmin) according to the distance from the position of the selected image signal, the product being obtained for each of the image signals included in the predetermined range.
Moreover, in this invention, the image signal is output as a sample point in the predetermined sampling interval, and an interpolation is performed on an arbitrary point in a cycle equal to or less than the predetermined sampling interval by an interpolation method using a conversion including the linear combination of a plurality of the sample points located in the vicinity of the arbitrary point. This interpolation method includes a weighting operation using the plurality of the sample points.
Furthermore, in this invention, the position of the object is measured on the basis of the interpolated image signal. Herein, the predetermined sampling interval is determined on the basis of the amount of position measurement error in the measurement. The object predetermined herein is a substrate onto which a circuit pattern is transferred, and the amount of position measurement error in the predetermined sampling interval is the value where a total overlay becomes xc2xc or less of the minimum line width of the circuit pattern transferred onto the substrate.
Still further, in this invention, the interpolation is performed on the image signal itself and on a correlation function obtained on the basis of the image signal.
In order to accomplish the foregoing objects, a second mark detection method of the present invention comprises the steps of: imaging a mark formed on an object; converting an image of the mark, which is formed on an image pickup device, into an electrical image signal; outputting a signal related to the image signal in a predetermined sampling interval as a sample point; and performing an interpolation on an arbitrary point in a cycle equal to or less than the predetermined sampling interval by an interpolation method using a conversion including the linear combination of a plurality of the sample points.
Herein, in the interpolation method, the arbitrary point is subjected to interpolation using the plurality of the sample points located in the vicinity of the arbitrary point. This interpolation method includes a step of performing a weighting operation using the plurality of the sample points, and an interpolation filter for determining a weighting coefficient used in the weighting operation. Herein, when the predetermined sampling interval is T, the interpolation filter includes an interpolation function s(dx) given by as:       s    ⁡          (      dx      )        =            sin      ⁡              (                  2          ⁢                      xe2x80x83                    ⁢          π          ⁢                      xe2x80x83                    ⁢                      dx            /            2                    ⁢          T                )                    2      ⁢              xe2x80x83            ⁢      π      ⁢              xe2x80x83            ⁢              dx        /        2            ⁢      T      
The interpolation filter is represented as: S(dx)=s(dx)xc2x7W(dx). S is a product of the interpolation function s(dx) and a window function W(dx) which is capable of converging an end portion of the interpolation function s(dx) to zero. Herein, when a length of the window is R, the window function W(dx) is represented as:       W    ⁡          (      dx      )        =            1      +              cos        ⁡                  (                      2            ⁢                          xe2x80x83                        ⁢            π            ⁢                          xe2x80x83                        ⁢                          dx              /              R                                )                      2  
Moreover, the second mark detection method of the present invention standardizes the interpolation filter so that the sum total of the weighting coefficients used when a first arbitrary point is subjected to interpolation and the sum total of the weighting coefficients used when a second arbitrary point different from the first arbitrary point is subjected to interpolation can be predetermined values. Herein, the standardization converts the respective coefficients of the interpolation filter by dividing the respective coefficients by the sum total of the respective coefficients.
Furthermore, the second mark detection method of the present invention performs a smoothing process for removing a component having a cycle equal to or less than a predetermined cycle from the image signal output as a sample point in the predetermined sampling interval. Herein, the image pickup device has a pixel size Ps a predetermined multiple of the minimum periodic component Pmin of the image formed on the image pickup device. The smoothing process includes a step of removing a periodic component equal to or less than 1/(1/Psxe2x88x921/Pmin), on the basis of the pixel size Ps and the minimum periodic component Pmin. The pixel size Ps is larger than 0.5 times the minimum periodic component Pmin.
Furthermore, the interpolation is performed on the image signal itself.
The exposure method of the present invention is characterized in that the object is a substrate onto which a predetermined pattern is transferred, and the predetermined pattern is transferred onto the substrate which is aligned on the basis of the mark detected by the use of the mark detection method.
Moreover, a device manufacturing method of the present invention is for manufacturing a device using the exposure method of transferring the predetermined pattern onto the substrate.
A first mark detection apparatus of the present invention includes an irradiation system which irradiates a mark formed on an object with a detection beam, an image-forming system which forms an image of the mark on the image-forming surface, and an image pickup device disposed above the image-forming surface, a sampling device which converts the image of the mark into an electrical image signal in order to output a signal related to the image signal in a predetermined sampling interval, and an interpolation device which interpolates the signal related to the image signal in a cycle equal to or less than the predetermined sampling interval.
Herein, the first mark detection apparatus of the present invention is characterized in that the image pickup device has a pixel size a predetermined multiple of the minimum periodic component of an image formed on the image-forming surface, the predetermined sampling interval includes a cycle of the pixel size, and the interpolation device performs an interpolation in a cycle equal to or less than the pixel size. The minimum periodic component is defined by xcex/2NA based on the wavelength xcex of the detection beam and the numerical aperture NA of the image-forming system. The pixel size is preferably 0.2 to 0.5 times the minimum periodic component. In addition, the first mark detection apparatus of the present invention further comprises a smoothing device which removes a component equal to or less than a predetermined cycle from a signal output at the sampling intervals by the sampling device. Herein, the pixel size Ps is larger than 0.5 times the minimum periodic component Pmin, and the smoothing device removes periodic components equal to or less than 1/(1/Psxe2x88x921/Pmin), on the basis of the pixel size Ps and the minimum periodic component Pmin.
Moreover, the first mark detection apparatus of the present invention is characterized in that the sampling device outputs a signal related to the image signal as a sample point in the predetermined sampling interval, and the interpolation device interpolates an arbitrary point in a cycle equal to or less than the predetermined sampling interval by an interpolation method using a conversion including the linear combination of a plurality of the sample points located in the vicinity of the arbitrary point.
Furthermore, the first mark detection apparatus further comprises a measurement device which measures a position of the object on the basis of the interpolated signal, characterized in that the predetermined sampling interval is determined on the basis of the amount of position measurement error of the measurement by the measurement device.
Still further, the first mark detection apparatus is characterized in that the sampling device outputs the image signal itself in the predetermined sampling interval, and the interpolation device performs an interpolation on the image signal itself.
A second mark detection method of the present invention comprises a sampling device which images a mark formed on an object, converting an image of the mark into an electrical image signal and outputting a signal related to the image signal in a predetermined sampling interval as a sampling point; and an interpolating device which interpolates an arbitrary point in a cycle equal to or less than the predetermined sampling interval by an interpolation method using a conversion including the linear combination of a plurality of the sample points. Herein, the interpolation device interpolates the arbitrary point using the plurality of the sample points located in the vicinity of the arbitrary point, and the interpolation device performs a weighting operation using the plurality of the sample points, and includes an interpolation filer which determines a weighting coefficient used in the weighting operation. When the predetermined sampling interval is T, this interpolation filter includes an interpolation function s(dx) represented as:       s    ⁡          (      dx      )        =            sin      ⁡              (                  2          ⁢                      xe2x80x83                    ⁢          π          ⁢                      xe2x80x83                    ⁢                      dx            /            2                    ⁢          T                )                    2      ⁢              xe2x80x83            ⁢      π      ⁢              xe2x80x83            ⁢              dx        /        2            ⁢      T      
Moreover, the first mark detection apparatus of the present invention further comprises a standardizing device which standardizes the interpolation filter so that the sum total of the weighting coefficients used when interpolation is performed on a first arbitrary point and the sum total of weighting coefficients used when interpolation is performed on a second arbitrary point different from the first arbitrary point can be predetermined values. This standardizing device converts the respective coefficients of the interpolation filter by dividing the respective coefficients by the sum total of the respective coefficients.
Furthermore, the first mark detection apparatus of the present invention further comprises a smoothing device which removes a component equal to or less than a predetermined cycle from the signal output as a sample point in the predetermined sampling interval by the sampling device. Herein, the sampling device includes an image pickup device having a pixel size Ps of a predetermined multiple of the minimum periodic component Pmin of an image formed on a predetermined image-forming surface, and the smoothing device removes a periodic component equal to or less than 1/(1/Psxe2x88x921/Pmin), on the basis of the pixel size Ps and the minimum periodic component Pmin. This pixel size Ps is preferably larger than 0.5 times the minimum periodic component Pmin.
In addition, the second mark detection apparatus of the present invention is characterized in that the sampling device outputs the image signal itself in the predetermined sampling interval, and the interpolation device performs an interpolation on the image signal itself.
The exposure apparatus of the present invention is characterized in that the object is a substrate onto which a predetermined pattern is transferred, and the predetermined pattern is transferred onto the substrate which is aligned on the basis of the mark detected by the use of the mark detection apparatus.
Furthermore, a device of the present invention is manufactured through the step of transferring the predetermined pattern onto the substrate by the exposure apparatus.